On the spatially asymptotic structure of time-periodic solutions to the Navier-Stokes equations

TL;DR

This paper investigates the large-distance behavior of weak time-periodic solutions to the Navier-Stokes equations with a drift term, revealing that asymptotics are governed by Oseen fundamental solutions.

Contribution

It provides a detailed asymptotic analysis of time-periodic Navier-Stokes solutions, including expansions for velocity and gradients, highlighting the role of Oseen solutions at infinity.

Findings

Asymptotic expansions for velocity and gradients are derived.

Spatial infinity behavior is characterized by Oseen fundamental solutions.

The decomposition into steady and remaining parts clarifies the structure of solutions.

Abstract

The asymptotic behavior of weak time-periodic solutions to the Navier-Stokes equations with a drift term in the three-dimensional whole space is investigated. The velocity field is decomposed into a time-independent and a remaining part, and separate asymptotic expansions are derived for both parts and their gradients. One observes that the behavior at spatial infinity is determined by the corresponding Oseen fundamental solutions.